inequalities and word problems

Question

A chemist mixes a silver alloy AG1 costing $13 per ounce with another silver alloy AG2 costing $17 per ounce to make 10 oz of a new alloy. If the chemist wants the new alloy to cost between $15 and $16 per ounce, how many ounces of AG1 should the chemist use?

Answer 1

This problem is solved by using the formula

C1V1 + C2V2 = C3V3, where C =  Concentration and V = Volume

 

In this case, alloy AG1 will be used to dilute alloy AG3 to produce alloy AG3

 

Let x = Volume of AG2, then

 

x$17 + (10oz - x)$13 = 10oz$15

 

$17x +$130oz - $13x = $150oz

 

Combining terms, we get $4x = $20oz

 

Solving, x = 5oz

Thus, mixing 5oz of AG1 at $17 with 5oz at $13 of AG2 will produce 10oz of AG3 at $15.

 

Proof, 5(17) + 5(13) = 10(15); $85 + $65 = $150